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<H3>pair_style resquared command 
</H3>
<H3>pair_style resquared/gpu command 
</H3>
<H3>pair_style resquared/omp command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>pair_style resquared cutoff 
</PRE>
<UL><LI>cutoff = global cutoff for interactions (distance units) 
</UL>
<P><B>Examples:</B>
</P>
<PRE>pair_style resquared 10.0
pair_coeff * * 1.0 1.0 1.7 3.4 3.4 1.0 1.0 1.0 
</PRE>
<P><B>Description:</B>
</P>
<P>Style <I>resquared</I> computes the RE-squared anisotropic interaction
<A HREF = "#Everaers">(Everaers)</A>, <A HREF = "#Babadi">(Babadi)</A> between pairs of
ellipsoidal and/or spherical Lennard-Jones particles.  For ellipsoidal
interactions, the potential considers the ellipsoid as being comprised
of small spheres of size sigma.  LJ particles are a single sphere of
size sigma.  The distinction is made to allow the pair style to make
efficient calculations of ellipsoid/solvent interactions.
</P>
<P>Details for the equations used are given in the references below and
in <A HREF = "PDF/pair_resquared_extra.pdf">this supplementary document</A>.
</P>
<P>Use of this pair style requires the NVE, NVT, or NPT fixes with the
<I>asphere</I> extension (e.g. <A HREF = "fix_nve_asphere.html">fix nve/asphere</A>) in
order to integrate particle rotation.  Additionally, <A HREF = "atom_style.html">atom_style
ellipsoid</A> should be used since it defines the
rotational state and the size and shape of each ellipsoidal particle.
</P>
<P>The following coefficients must be defined for each pair of atoms
types via the <A HREF = "pair_coeff.html">pair_coeff</A> command as in the examples
above, or in the data file or restart files read by the
<A HREF = "read_data.html">read_data</A> or <A HREF = "read_restart.html">read_restart</A>
commands:
</P>
<UL><LI>A12 = Energy Prefactor/Hamaker constant (energy units)
<LI>sigma = atomic interaction diameter (distance units)
<LI>epsilon_i_a = relative well depth of type I for side-to-side interactions
<LI>epsilon_i_b = relative well depth of type I for face-to-face interactions
<LI>epsilon_i_c = relative well depth of type I for end-to-end interactions
<LI>epsilon_j_a = relative well depth of type J for side-to-side interactions
<LI>epsilon_j_b = relative well depth of type J for face-to-face interactions
<LI>epsilon_j_c = relative well depth of type J for end-to-end interactions
<LI>cutoff (distance units) 
</UL>
<P>The parameters used depend on the type of the interacting particles,
i.e. ellipsoids or LJ spheres.  The type of a particle is determined
by the diameters specified for its 3 shape paramters.  If all 3 shape
parameters = 0.0, then the particle is treated as an LJ sphere.  The
epsilon_i_* or epsilon_j_* parameters are ignored for LJ spheres.  If
the 3 shape paraemters are > 0.0, then the particle is treated as an
ellipsoid (even if the 3 parameters are equal to each other).
</P>
<P>A12 specifies the energy prefactor which depends on the types of the
two interacting particles.
</P>
<P>For ellipsoid/ellipsoid interactions, the interaction is computed by
the formulas in the supplementary docuement referenced above.  A12 is
the Hamaker constant as described in <A HREF = "#Everaers">(Everaers)</A>. In LJ
units:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared.jpg">
</CENTER>
<P>where rho gives the number density of the spherical particles
composing the ellipsoids and epsilon_LJ determines the interaction
strength of the spherical particles.
</P>
<P>For ellipsoid/LJ sphere interactions, the interaction is also computed
by the formulas in the supplementary docuement referenced above.  A12
has a modifed form (see <A HREF = "PDF/pair_resquared_extra.pdf">here</A> for
details):
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared2.jpg">
</CENTER>
<P>For ellipsoid/LJ sphere interactions, a correction to the distance-
of-closest approach equation has been implemented to reduce the error
from two particles of disparate sizes; see <A HREF = "PDF/pair_resquared_extra.pdf">this supplementary
document</A>.
</P>
<P>For LJ sphere/LJ sphere interactions, the interaction is computed
using the standard Lennard-Jones formula, which is much cheaper to
compute than the ellipsoidal formulas.  A12 is used as epsilon in the
standard LJ formula:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared3.jpg">
</CENTER>
<P>and the specified <I>sigma</I> is used as the sigma in the standard LJ
formula.
</P>
<P>When one of both of the interacting particles are ellipsoids, then
<I>sigma</I> specifies the diameter of the continuous distribution of
constituent particles within each ellipsoid used to model the
RE-squared potential.  Note that this is a different meaning for
<I>sigma</I> than the <A HREF = "pair_gayberne.html">pair_style gayberne</A> potential
uses.
</P>
<P>The epsilon_i and epsilon_j coefficients are defined for atom types,
not for pairs of atom types.  Thus, in a series of pair_coeff
commands, they only need to be specified once for each atom type.
</P>
<P>Specifically, if any of epsilon_i_a, epsilon_i_b, epsilon_i_c are
non-zero, the three values are assigned to atom type I.  If all the
epsilon_i values are zero, they are ignored.  If any of epsilon_j_a,
epsilon_j_b, epsilon_j_c are non-zero, the three values are assigned
to atom type J.  If all three epsilon_i values are zero, they are
ignored.  Thus the typical way to define the epsilon_i and epsilon_j
coefficients is to list their values in "pair_coeff I J" commands when
I = J, but set them to 0.0 when I != J.  If you do list them when I !=
J, you should insure they are consistent with their values in other
pair_coeff commands.
</P>
<P>Note that if this potential is being used as a sub-style of
<A HREF = "pair_hybrid.html">pair_style hybrid</A>, and there is no "pair_coeff I I"
setting made for RE-squared for a particular type I (because I-I
interactions are computed by another hybrid pair potential), then you
still need to insure the epsilon a,b,c coefficients are assigned to
that type in a "pair_coeff I J" command.
</P>
<P>For large uniform molecules it has been shown that the epsilon_*_*
energy parameters are approximately representable in terms of local
contact curvatures <A HREF = "#Everaers">(Everaers)</A>:
</P>
<CENTER><IMG SRC = "Eqs/pair_resquared4.jpg">
</CENTER>
<P>where a, b, and c give the particle diameters.
</P>
<P>The last coefficient is optional.  If not specified, the global cutoff
specified in the pair_style command is used.
</P>
<HR>

<P>Styles with a <I>cuda</I>, <I>gpu</I>, <I>omp</I>, or <I>opt</I> suffix are functionally
the same as the corresponding style without the suffix.  They have
been optimized to run faster, depending on your available hardware, as
discussed in <A HREF = "Section_accelerate.html">Section_accelerate</A> of the
manual.  The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.
</P>
<P>These accelerated styles are part of the USER-CUDA, GPU, USER-OMP and OPT
packages, respectively.  They are only enabled if LAMMPS was built with
those packages.  See the <A HREF = "Section_start.html#start_3">Making LAMMPS</A>
section for more info.
</P>
<P>You can specify the accelerated styles explicitly in your input script
by including their suffix, or you can use the <A HREF = "Section_start.html#start_7">-suffix command-line
switch</A> when you invoke LAMMPS, or you can
use the <A HREF = "suffix.html">suffix</A> command in your input script.
</P>
<P>See <A HREF = "Section_accelerate.html">Section_accelerate</A> of the manual for
more instructions on how to use the accelerated styles effectively.
</P>
<HR>

<P><B>Mixing, shift, table, tail correction, restart, rRESPA info</B>:
</P>
<P>For atom type pairs I,J and I != J, the epsilon and sigma coefficients
and cutoff distance can be mixed, but only for sphere pairs.  The
default mix value is <I>geometric</I>.  See the "pair_modify" command for
details.  Other type pairs cannot be mixed, due to the different
meanings of the energy prefactors used to calculate the interactions
and the implicit dependence of the ellipsoid-sphere interaction on the
equation for the Hamaker constant presented here.  Mixing of sigma and
epsilon followed by calculation of the energy prefactors using the
equations above is recommended.
</P>
<P>This pair styles supports the <A HREF = "pair_modify.html">pair_modify</A> shift
option for the energy of the Lennard-Jones portion of the pair
interaction, but only for sphere-sphere interactions.  There is no
shifting performed for ellipsoidal interactions due to the anisotropic
dependence of the interaction.
</P>
<P>The <A HREF = "pair_modify.html">pair_modify</A> table option is not relevant
for this pair style.
</P>
<P>This pair style does not support the <A HREF = "pair_modify.html">pair_modify</A>
tail option for adding long-range tail corrections to energy and
pressure.
</P>
<P>This pair style writes its information to <A HREF = "restart.html">binary restart
files</A>, so pair_style and pair_coeff commands do not need
to be specified in an input script that reads a restart file.
</P>
<P>This pair style can only be used via the <I>pair</I> keyword of the
<A HREF = "run_style.html">run_style respa</A> command.  It does not support the
<I>inner</I>, <I>middle</I>, <I>outer</I> keywords of the <A HREF = "run_style.html">run_style
command</A>.
</P>
<HR>

<P><B>Restrictions:</B>
</P>
<P>This style is part of the ASPHERE package.  It is only enabled if
LAMMPS was built with that package.  See the <A HREF = "Section_start.html#start_3">Making
LAMMPS</A> section for more info.
</P>
<P>This pair style requires that atoms be ellipsoids as defined by the
<A HREF = "atom_style.html">atom_style ellipsoid</A> command.
</P>
<P>Particles acted on by the potential can be finite-size aspherical or
spherical particles, or point particles.  Spherical particles have all
3 of their shape parameters equal to each other.  Point particles have
all 3 of their shape parameters equal to 0.0.
</P>
<P>The distance-of-closest-approach approximation used by LAMMPS becomes 
less accurate when high-aspect ratio ellipsoids are used.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "pair_coeff.html">pair_coeff</A>, <A HREF = "fix_nve_asphere.html">fix nve/asphere</A>,
<A HREF = "compute_temp_asphere.html">compute temp/asphere</A>, <A HREF = "pair_gayberne.html">pair_style
gayberne</A>
</P>
<P><B>Default:</B> none
</P>
<HR>

<A NAME = "Everaers"></A>

<P><B>(Everaers)</B> Everaers and Ejtehadi, Phys Rev E, 67, 041710 (2003).
</P>
<A NAME = "Babadi"></A>

<P><B>(Berardi)</B> Babadi, Ejtehadi, Everaers, J Comp Phys, 219, 770-779 (2006).
</P>
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